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YEAR 3 · ADDITION AND SUBTRACTION · 18 MIN

Finding missing calculation values

Find an unknown part, whole or change in an addition or subtraction equation.

In this lesson

Before you start
  • Inverse operations
  • Addition and subtraction
01 / LEARN

Understand the idea.

What does the box stand for?

A box or question mark stands for an unknown number. First decide whether it represents a part or the whole. In 34+?=81, the whole is known and the missing number is the other added part.

To find a missing whole, add the known parts. To find a missing part, subtract the known part from the whole. A quick part–whole sketch can help you choose before calculating.

A missing starting number

In ?−28=46, the starting whole is missing. The 46 is what remains after removing 28, so add those two parts to rebuild the starting number: 46+28=74.

In 74−?=46, the whole is already given; the removed part is missing. Subtract 46 from 74 to find it. Put your answer back into the original sentence and check both sides agree.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find a missing added part

Find the missing number: 157 + ? = 300.

Worked solution

  1. 1

    Find the missing part by subtraction.

    ?=300−157

    The whole is three hundred and one of its parts is one hundred and fifty-seven.

  2. 2

    Remove one hundred, then fifty.

    300−100=200200−50=150

    These are the first two parts of one hundred and fifty-seven.

  3. 3

    Remove the final seven.

    150−7=143

    All of the known part has now been subtracted.

  4. 4

    Substitute the missing number.

    157+143=300

    The two added parts give the required whole.

Answer

143

EXAMPLE 02

Find a missing start

Find the missing number: ? − 67 = 125.

Worked solution

  1. 1

    Rebuild the missing starting whole.

    ?=125+67

    Add the removed sixty-seven to the remaining one hundred and twenty-five.

  2. 2

    Add sixty, then seven.

    125+60=185185+7=192

    Sixty and seven together make sixty-seven.

  3. 3

    Check in the original subtraction.

    192−67=125

    Removing the given amount leaves the required remainder.

Answer

192

03 / YOUR TURN

Try it yourself.

Check your understanding

Find ?: ? − 19 = 42.

Show answer & reasoning

61

The missing starting number must contain both the remaining 42 and removed 19. Add 42+19=61; checking gives 61−19=42.

Keep practising

6 worksheet questions

Read the questions online
  1. Find ?: 38+?=70.
  2. Find ?: ?+46=125.
  3. Find ?: 93−?=57.
  4. Find ?: ?−48=164.
  5. A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?
  6. Find a number that makes this equation true: 25+?=18+32.
Read the worked solutions
  1. Find ?: 38+?=70.

    70−38=32; check 38+32=70.

    32
  2. Find ?: ?+46=125.

    125−46=79.

    79
  3. Find ?: 93−?=57.

    93−57=36; check 93−36=57.

    36
  4. Find ?: ?−48=164.

    164+48=212; check 212−48=164.

    212
  5. A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?

    ?−12=27; 27+12=39.

    39 people
  6. Find a number that makes this equation true: 25+?=18+32.

    First find the right side: 18+32=50. Then 50−25=25. Check both sides equal 50.

    25
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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.

Official curriculum source ↗

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